Kepler

1
Keplers 1st Law of Planetary Motion.
The Sun is not at the center of the ellipse, but
is instead at one focus (generally there is
nothing at the other focus of the ellipse). The
planet then follows the ellipse in its orbit,
which means that the Earth-Sun distance is
constantly changing as the planet goes around its
orbit.
2
The line joining the Sun and planet sweeps out
equal areas in equal times, so the planet moves
faster when it is nearer the Sun. Thus, a planet
executes elliptical motion with constantly
changing angular speed as it moves about its
orbit. The point of nearest approach of the
planet to the Sun is termed perihelion the point
of greatest separation is termed aphelion. A
planet moves fastest when it is near perihelion
and slowest when it is near aphelion.
3
Kepler's Third Law
In this equation P represents the period of
revolution for a planet and R represents the
length of its semimajor axis. Kepler's Third Law
implies that the period for a planet to orbit the
Sun (P) increases rapidly with the radius (R) of
its orbit. So, we can now use Keplers 3rd Law to
discover that Mercury, the innermost planet,
takes only 88 days to orbit the Sun but the
outermost planet (Pluto) takes 248 years to do
the same.
4
Simplifying Keplers 3rd Law

• The period (P) of Earth is one year
• The average distance from the Earth to the Sun
  (semi-major axis R) is 1 AU
• Keplers 3rd law now becomes
• P12 R13
• ------ ------- or P12
  R13
• 1 year 1 AU

5
Examples of Keplers 3rd Law.
A planet named Moe orbits the Sun at a distance
of 4 AU. A second asteroid named Barney orbits
the Sun at 8 AU. Which asteroid will take longer
to go around the Sun? How much longer?
P12 R13
How much longer? 22.62/8 2.83 times
6
Example 2

• The period of Jupiter is 11.86 years. What is
  Jupiters average distance from the sun
• PJupiter2 RJupiter3
• 11.862 R3
• 140.66 R3

• RJupiter 5.20